Ruminations on architecture, from Ken Allinson
Tag Archives: Platonic solids
May 11, 2012Posted by on
I mentioned my friend Chall in an earlier mail (Open House Roma). Well, as his train heads northward through Europe our occasional email correspondence has continued. Milan, it seems, has been an unexpected pleasure. The Academy let him drop into life-drawing class … Happiness is …
In between that kind of chit-chat we discursively fenced with one another regarding some familiar old topics. Some were rather old. Very old.
As a young post-grad artist from St Martins, sucking on the blue Gauloises (which, I confess, we both enjoyed), Chall made a notable photograph for Keith Critchlow that is still reproduced, usually accompanied by contention: five Neolithic Scottish stone balls.
The claim (made in Critchlow’s's book, Time Stands Still: New Light on Megalithic Science (1979)), was that neolithic culture may have been more advanced than had been previously appreciated. In Chall’s words: “… it’s the finding of the dodeca stone ball that’s caused the fuss … It implies the discovery of the golden mean and ‘irrational’ numbers – like pi and root 2 and 3 – that occur in the form and behaviour of all living organisms in the universe from galactic spirals to the Fibonacci series, which are considered integral to our definition of Life … All living organism number is expressed in the dodecahedron as all of space can be defined by only 12 Great Circle divisions. Five Platonic solids – all symmetrical and all described by the intersection of twelve equal circles that transcribe a sphere are all the elements required to describe and understand how space works. … If we wanted to understand the nature of how space behaves then these are the building blocks. And these are controlled by a numerical sequence that cannot be resolved – another way of describing infinity.”
To say Keith and Chall’s claim has been contentious would be an understatement. Becasue of issue concerning the last of the two balls in the photo they have been accused of concocting a hoax – not a possible misreading, but a hoax.
If you knew these two characters you would appreciate that the fabrication of a hoax is not merely unlikely, but so offensive that their blood boils in indignation. When the accusation was first made – to their faces – it was a long time ago and much time has passed … Except that the contention continues on web pages. Why, it is argued, did Chall not record the catalogue numbers of the balls? where are they now? Why? Because Chall has never claimed the pretension of being a scholar rather than an enthusiastic co-worker who had a background in performance art at St Martin’s, someone assisting his mentor in a fringe arena of enquiry. It’s a familiar story: someone sees things in a different way, breaks out of the orthodoxy … It happens all the time, but there are always a lot of vested interests at stake.
Within the deep dark heart of this discourse is, of course, the search for meaning: an anxiety concerning the most fundamental aspects of that meaning and an aspiration to ‘come home’ in the sense of concocting, not a hoax, but a place of deliverance, resolution and reassurance. Of peace. In this syndrome something is lost: God, self, knowledge of the underlying patternings of a designed universe … and is to be refound. In Platonic terms, this is a re-membering: we are reunited, made into a whole body again. In Christian terms we are saved. We all suffer this malady, and there isn’t any cure. Collectively, we stand on the station platform, getting onto this or that train, wondering which one to board, wondering why the intended one is late … and we watch sometimes bewildered passengers (occasionally with entourages) alighting in bemusement that this is where they started a long time ago.
Anyway, that is not my real point here.
My bottom-line is that, believe it or not, although I am intrigued, I’m relatively indifferent to this debate. For me, it comes too close to an even older pretension: access to an otherwise concealed knowledge and the benefits thus to be derived. Most of architecture’s historic icons are embodiments of this value, viz good architecture as works of reassurance as well as commodity and delight. Thus the true, underlying issue within the discourse is possibly not knowledge per se but active intersubjective relations and power structures, especially in the guise of a priestly class among bodies of hunters and their women (the true bearers of culture!). Thorstein Veblen again comes to mind, referencing the meaning of conspicuous consumption, and also Bataille, with his references to the ritualistic principle of potlatch (though these outlooks upon creative endeavour hardly figure in discourse upon geometry in architecture).
My interest is particularly aroused by how such disclosures were played out during the European Renaissance, at the beginnings of modernism, when the likes of Copernicus and Kepler were manifesting a transition to new kinds of world-view that never quite left the old ones behind. (Yes, I am as intrigued by the notion of ‘roots’ to what we believe as anyone else …)
From this viewpoint I am, personally, not convinced that my friend Chall and his life-long mentor have really left this historic space of action, that they aren’t still rattling around in it (much to the delight of Critchlow’s biggest fan HRH Prince Charles, who walks in the gardens of Highgrove with courtiers who not only assure him of his Divine Right, but also that the masses are a herd suffering the laws of large numbers and awaiting his reign as a neo-Platonic philosopher king). Critchlow speaks, for example, of a lost inner (hermeneutic) knowledge and its replacement by exterior forms of knowledge, but this is really a way of contrasting what others have discussed in terms of a horizontal enquiry as opposed to a traditional vertical (or anagogical) enquiry. In fact, I doubt if his belief has altered since 1979, when he wrote of archetypal images as an a priori patterning which man should imitate: “Mankind confirms his own grounds for being by his capability of conceiving this archetypal pattern, and sustains his world by re-creating it in that world.” This is, in itself, a paradoxical message, as if mankind somehow stood outside of Creation or genuinely is ‘fallen’ and suffers a blindness which confirms a need to go ladder-climbing.
Well, I can be witness to my own irrational beliefs as well – a conviction that, much as I respect, this tradition and those who work in it, they’ve got it wrong. My preference is for Aristotle rather than Plato (philosphers tell us we all seem to end up on one side of the fence or the other). Whilst never denying the import of contemplation of the divine, to aristotle the Platonic notion of a reality beyond or outside of experience was rather absurd: being and becoming intermix and ultimately elude a definitiveness of rational grounding – that, for us, is the point. A realm of the Customary (as architects such as, in the C17th, Perrault and Wren termed it) may seemingly bind us and frustrate reason’s ‘freedoms’, but every lived freedom must forever determine solid ground for its feet and necessity (what the Renaissance dealt with as the principle of ‘sufficient reason’) as its telos. Even for the mature Plato of Phaedrus the intellect must be counterbalanced by Eros, by the passions and the actions inspired by them. As Martha Nussbaum puts it, “[w]e advance toward understanding by pursuing and attending to our complex appetitive/emotional responses to the beautiful; it would not have been accessible to the intellect alone.”
Etymologically, the word truth means ‘what is revealed or brought out from concealment’ and, as employed by Plato, referred to stable and privileged, unhypothetical viewpoint to be contrasted with normal human experience. For Aristotle, the latter, as phainomena or ‘appearances’, was a body of observed facts and opinions outside of which it is humanely impossible to stand. This may worry the Platonist, but Aristotle was referring us to the need, through intellectual habituation, to develop the nous, or perspicacity, which enables us to appreciate truth as what is inside the circle of experience, not outside, behind or beyond language and life. It is nous that enables us to get to the arché (root) or secure starting point, of how we must live with appearances and their challenges. The point was not to purchase a ticket on some express train to where things are more-real-than-real, but to stay on the platform and flourish by addressing demands for the exercise of practical wisdom. It was, as it were, to get horizontal and therein find whatever is vertical … Or whatever.
This vertical / horizontal juxtaposition was what the life and work of Johannes Kepler, for example, was all about. Unlike Fludd, Kepler was convinced that God’s design had to be verifiable: “What he [Fludd] borrows from the Ancients, I derive from the Nature of things, and I constitute it from its very foundations.” Nevertheless, this was quite a disturbing issue, one that Copernicus had instigated: a challenge to ‘speculative’ inquiry deriving from the implication that idealistic presumptions (usually anagogical, i.e.’ vertical’) might never correspond to what horizontal enquiry disclosed to be the case. Kepler, unfortunately, may have been stretching himself in both directions at once, but he was determined to proceed “according to the laws of Nature.” In place of Fludds’s neo-Kabbalistic ‘play’, Kepler commented that, “I play in such a way that i do not forget that i am playing. For we can prove nothing by symbols, we can discover no secret in natural philosophy by geometric symbols, unless they agree with established facts.” Ultimately, this (as pointed out by Fernand Hallyn, in The Poetic Structure of the world, a book I highly recommend) became a dissociation between form and image, between the tangible and the intelligible. Suddenly, it was as if the ‘monstrosity’ of the seen and experienced world could no longer be ‘saved.’ Fludd could no longer have the earth at the heart of a geocentric universe (earth, water, air, fire, etc, upward toward the angels and the divine); the sun was apparently at the centre. As Panofsky put it, “that which in the past had seemed unquestionable was thoroughly problematical: the relationship of the mind to reality as perceived by the senses.” How was one to deal with the semiotics of this new universe?
It is possible that we can no longer appreciate how disturbing all this was. As MacIntyre laments, we have swung to some opposite pole of belief, expressing (especially moral) beliefs that can find no rational foundation. Meanwhile, infinity is evermore important; it is crucial, for example, to the maths that keeps data flying around the internet. As with Levinson, even sceptical old Marxists such as Terry Eagleton now turn us toward an intersubjective caring for the Other in the form of another kind of infinity: love (cf. The Meaning of Life: A Very Short Introduction).
Meanwhile, while mathematicians simply accept infinity and employ it, my friend finds his own kind of consolation in geometry and, in that, number and the mysterious incommensurables for which the ancient Greek who discovered them was reportedly taken out on a ship and thrown overboard … or was it some Neolithic genius? Infinity as geometry, love or a feature of some complex mathematical equation – I’m not sure it matters. We take different trains, leaving from different platforms .. and all seem to end up in the same place.